2007/05/21 by L. Bertini, Lorenzo Bertini, Bertini, L. +12
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0705.2996
4 pages
arxiv created 2007/05/21 · openalex publication_date 2007/05/21 · arxiv updated 2015/12/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Experiments show that macroscopic systems in a stationary nonequilibrium state exhibit long range correlations of the local thermodynamic variables. In previous papers we proposed a Hamilton-Jacobi equation for the nonequilibrium free energy as a basic principle of nonequilibrium thermodynamics. We show here how an equation for the two point correlations can be derived from the Hamilton-Jacobi equation for arbitrary transport coefficients for dynamics with both external fields and boundary reservoirs. In contrast with fluctuating hydrodynamics, this approach can be used to derive equations for correlations of any order. Generically, the solutions of the equation for the correlation functions are non-trivial and show that long range correlations are indeed a common feature of nonequilibrium systems. Finally, we establish a criterion to determine whether the local thermodynamic variables are positively or negatively correlated in terms of properties of the transport coefficients.